On minimum energy control of commutative bilinear systems

A minimum energy control problem is considered for commutative bilinear systems with and without terminal constraints. Optimal controls are shown to be constant vectors determined by the boundary conditions. Sufficient conditions are derived for uniqueness of the optimal control in the absence of a terminal constraint. A class of physical bilinear systems is discussed which possesses the commutative property.     

Closed-loop control of stochastic non-linear systems

A new approach for optimum control of stochastic non-linear systems is developed from practical engineering assumptions. Systems amenable to this new approach include optimum guidance and navigation systems for space and terrestrial vehicles, optimum closed-loop process controllers and optimum controllers for systems with unknown parameters. The classical quadratic synthesis approach—optimization of a deterministic cost and perturbation estimation and control about that solution—is shown to give 24 per cent more cost and 97 per cent more mean-squared terminal error than the combined optimization approach presented for a sample problem involving control of a first-order system with an unknown time constant. A similar improvement in terminal error is shown for an atmospheric entry problem. Furthermore, the optimum controller automatically designs the best controller to minimize the effects of the unknown parameter without artificial augmentation of the cost function as is done in the sensitivity theory approach. The solution is obtained by expansion of the cost function in a power series around a deterministic trajectory with the assumption of linear perturbation estimation and control about that trajectory. Optimization of the expanded cost function gives necessary conditions dependent on the covariance matrices and the deterministic portion of the cost. When the necessary conditions are solved, a set of open-loop controls, perturbation controller gains, and perturbation estimator gains are obtained that can be precomputed and implemented into the system.     

On the theory of state-covariance assignment for single-inputlinear discrete systems

An alternative method for state-covariance assignment for discrete single-input linear systems is proposed. This method is based on the inverse solution of the Lyapunov equation, and the resulting formulas are similar in structure to the formulas for pole placement. Further, the set of all covariance matrices assignable to a single-input discrete system is also characterized. The proposed method is illustrated by a numerical example     

General response formula and minimum energy control for the generalsingular model of 2-D systems

The general response formula for the general singular model of 2-D linear systems is derived. The concepts of local reachability and local controllability are extended to the singular model. Necessary and sufficient conditions for local reachability and local controllability are established. The minimum energy control problem for the singular model is formulated and solved     

Closed-loop sensitivity reduction of linear optimal control systems

Inequalities are derived which demonstrate the reduction of sensitivity to plant-parameter variations of closed-loop linear optimal systems (as compared to nominally equivalent open-loop systems) according to a particular measure of sensitivity. The shortcomings of some other measures of sensitivity are discussed and illustrated in numerical examples. Numerical results for the sensitivity comparison of a first-order system and a third-order pitch-axis control system are given.     

Matrix minimum principle for distributed parameter control systems

It is shown that the matrix minimum principle can be used to study both deterministic and stochastic control systems described by partial differential equation models. It in shown that the matrix formulations of the control problem reduce to a state canonical equation which is identical with the Riccati equation of the conventional state vector representation. The technique employs the powerful optimization techniques of the calculus of variations and dynamic programming, and leads in a natural way to the separation principle for the case of stochastic optimal control problems. The results of this study show once more the close relationship between the tools used for finite-dimensional control problems and their distributed-parameter (infinite-dimensional) counterparts.     

具有结构不确定性的时滞系统的闭环鲁棒预测控制器

针对具有结构不确定性的时滞系统,设计了闭环鲁棒预测控制算法.该控制算法基于控制不变集方法,通过采用双模控制和闭环控制策略,增加了控制设计的自由度,进而扩大了系统的初始可行域并能获得较优的控制性能.仿真结果验证了该方法的有效性.     

Evolving performance control systems for digital puppetry

We describe a new approach for creating performance control systems for digital puppetry. Genetic programming with fitness values specified directly by the puppeteer is used. A generic device and model representation combined with the inherent domain independence of the genetic programming paradigm allows this approach to create control systems for arbitrary combinations of input devices and models. In addition, a number of unique interaction techniques have been developed to support the user‐directed search. In this paper we introduce the approach, describe the implementation and user interface and present the results from a comprehensive evaluation with expert users. We show that a search‐based approach can provide an effective alternative to manually designing performance control systems and an elegant mechanism for unifying low‐level input devices with a broad range of model control modes. Copyright © 2000 John Wiley & Sons, Ltd.     

Decentralized control of sequentially minimum phase systems

Fundamental limitations in decentralized control of systems with multivariable zeros are considered. It is shown that arbitrary bandwidth can be obtained with a stable block-diagonal controller, if certain subsystems of the open-loop system fail to have zeros in the right half-plane and a high-frequency condition holds. Implications on control structure design and sequential loop-closuring methods are discussed     

Solutions of minimum time problem and minimum fuel problem for discrete linear admissible control systems

In this paper the minimum time problem and the minimum fuel problem for discrete linear admissible control systems arc formulated (is one linear programming problem with two different objective functions. It is found that the obtained problem is very similar to the dual form of the linear programming problem for the discrete linear L₁ approximation problem. An efficient dual simplex algorithm for the latter problem is used with the necessary modification* to obtain the solution of either of the former problems. Numerical results show that the present, method compares favourably with other known methods.     

Ideal state reconstructor for deterministic digital control systems

A new state reconstructor for deterministic digital control systems is presented which is ideal in the following sense: if the plant parameters are known exactly, the output of the new state reconstructor will exactly equal the true state of the plant, not just approximate it. Furthermore, this ideal state reconstructor adds no additional states or eigenvalues to the system, nor does it affect the plant equation for the system in any way; it affects only the measurement equation. While there are countless ways of choosing the ideal state reconstructor parameters, two distinct methods are described here. An example is presented which illustrates the procedures for completely designing the ideal state reconstructor using both methods.     

Equivalent discrete optimal control problem for randomly sampled digital control systems

This paper considers the transformation of the optimal digital control problem to en equivalent discrete-time optimal control problem in the case of deterministic and stochastic sampling. The continuous-time system to be controlled is linear and disturbed by additive continuous-time white noise (not necessarily gaussian). The observations available at the sampling instants are in general non-linear and corrupted by discrete-time noise independent of the system noise (not necessarily additive, white or gaussian). The performance criterion is quadratic and an integral rather than a sum.     

Closed-loop multilevel control of large nonlinear systems via invariant imbedding techniques

An efficient multilevel control technique is developed whereby the closed-loop control policy is derived for a wide class of large non-linear dynamic systems using the invariant imbedding algorithms. The basic idea behind the developed technique is the decomposition-coordination procedure of hierarchical multilevel systems theory. Modification of the local subproblems at the first level results in the requirement of solving essentially the dynamic state equations as well as the Ricatti-like ordinary matrix equations. At the second level the coordinator updates the intervention parameters using a conjugate gradient algorithm. A principal feature of the developed technique is reflected in the possibility of being implemented in a real-time. Computer simulation of practical system applications greatly supports the potentiality of the developed two-level optimization technique.     

Quantization errors in digital control systems

An analytic study was conducted to develop a quantitative expression for the errors due to quantization (round-off) in digital control systems. An upper bound on the error in the output that was caused by quantization became available for two different sampling rates by describing a typical digital control system in terms of its state variables. The amount of the error introduced in the output by any one quantization operation was found to depend upon the sampling rate, system time constants, and the form of the controller chosen for system compensation. For a third-order plant, preceded by a zero-order hold circuit and compensated by a controller that provided a response dominated by a closed-loop pole pair with a damping ratio of 0.7, the error due to quantization was determined to be approximately ten times the value of the quantizing level. The error was reduced to six times the quantizing level by increasing the sampling rate by a factor of 2, to 20 per second. The results of the study furnished a convenient procedure for analyzing quantization in a digital control system and led to a specification on the precision required in the digital controller and the necessary encoding equipment.     

Closed-loop stable model predictive control of integrating systems with dead time

Model predictive control (MPC) applications in the process industry usually deal with process systems that show time delays (dead times) between the system inputs and outputs. Also, in many industrial applications of MPC, integrating outputs resulting from liquid level control or recycle streams need to be considered as controlled outputs. Conventional MPC packages can be applied to time-delay systems but stability of the closed loop system will depend on the tuning parameters of the controller and cannot be guaranteed even in the nominal case. In this work, a state space model based on the analytical step response model is extended to the case of integrating time systems with time delays. This model is applied to the development of two versions of a nominally stable MPC, which is designed to the practical scenario in which one has targets for some of the inputs and/or outputs that may be unreachable and zone control (or interval tracking) for the remaining outputs. The controller is tested through simulation of a multivariable industrial reactor system.     

The relationship between minimum entropy control and risk-sensitivecontrol for time-varying systems

The connection between minimum entropy control and risk-sensitive control for linear time-varying systems is investigated. For time-invariant systems, the entropy functional and the linear exponential quadratic Gaussian cost are the same. In this paper, it is shown that this is not true for general time varying systems. It does hold, however, when the system admits a state-space representation     

A simplex algorithm for minimum fuel problems of linear discrete control systems

A simplex algorithm for solving the minimum fuel problem for linear discrete control systems is described. In this algorithm an initial basic feasible solution is available with no artificial variables needed. Also minimum computer storage is required. The algorithm is a simple and fast one. A numerical example is given     

Direct digital modal control of cascaded-vehicle systems

In this paper control laws for the direct digital control of cascaded-vehicle systems are derived on the basis of modal control theory. These laws are analogous to these previously obtained by Porter and Crossley (1970) for the continuous-time modal control of such systems.     

Testing and evaluation of digital control systems

Testing procedures for analogue instruments are described as well as for controllers and control systems based on the use of microprocessors. The paper compares the difference between system testing and testing of system elements. The difference between digital and analogue evaluations are also described. The dynamic response to various and nonlinear algorithms are both shown and explained.